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Resolutions over Koszul algebras

Authors
  • Green, Edward L.1
  • Hartman, Gregory2
  • Marcos, Eduardo N.3
  • Solberg, Øyvind4
  • 1 Virginia Tech, Department of Mathematics, Blacksburg, VA, 24061, USA , Blacksburg
  • 2 The University of Arizona, Department of Mathematics, Tucson, AZ, 85721-0089, USA , Tucson
  • 3 Universidade São Paulo Cidade Universitária, Instituto de Matemática e Estatística, São Paulo, CEP 05508-090, Brazil , São Paulo
  • 4 NTNU, Institutt for matematiske fag, Trondheim, N-7491, Norway , Trondheim
Type
Published Article
Journal
Archiv der Mathematik
Publisher
Birkhäuser-Verlag
Publication Date
Aug 01, 2005
Volume
85
Issue
2
Pages
118–127
Identifiers
DOI: 10.1007/s00013-005-1299-9
Source
Springer Nature
Keywords
License
Yellow

Abstract

In this paper we show that if \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Lambda = \mathop \coprod \limits_{i \geqq 0} \Lambda _i $$\end{document} is a Koszul algebra with Λ0 isomorphic to a product of copies of a field, then the minimal projective resolution of Λ0 as a right Λ-module provides all the information necessary to construct both a minimal projective resolution of Λ0 as a left Λ-module and a minimal projective resolution of Λ as a right module over the enveloping algebra of Λ. The main tool for this is showing that there is a comultiplicative structure on a minimal projective resolution of Λ0 as a right Λ-module.

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